Multibody Solver Research Articles

Towards blade-resolved ice accretion simulations of flexible blades using mixed-fidelity models

We present a modular framework for blade-resolved fluid-structure interaction simulations of rotors. The framework is based on the coupling of the multi-body solver MBDyn with the fluid solver SU2 using the library preCICE. A preliminary validation is carried out against other open-source codes analysing the UAE Phase VI experiment. In the future, the framework will be used to study ice accretion on flexible blades. Indeed, blade flexibility has not been considered yet in the numerical modelling of ice accretion due to lacking computational tools and high computational costs. A first application on ice accretion is shown by analyzing the temporal evolution of the modal frequencies of an isolated blade during an icing event simulated numerically with a quasi-3D approach. The results provide insight into the nature of ice throw from wind turbines.

3D SPH analysis of focused waves interacting with a floating structure

In recent years, the number of offshore floating structures has been growing and is expected to continue growing. Due to climate change, the frequency and severity of extreme waves are increasing. Numerical models can be a strategic tool in the reliable design and optimization of marine structures. However, the number of numerical parameters to be tuned plays a crucial role, as they could limit the model’s applicability and reliability. Furthermore, there are many challenges in modelling wave-structure interaction. Among these challenges, the simulation of one-dimensional tethers is of great concern when dealing with moored floating structures. In this study, a 3D numerical model is developed based on the Smoothed Particle Hydrodynamics (SPH) technique. This hydrodynamic model is coupled with a multi-body solver for the dynamic analysis of moorings and structures. In a three-dimensional numerical flume, focused ocean waves are generated with a piston-type wave-maker and propagated until impact with the floating structure. The developed model predicts the wave profile, impact forces, and structural dynamics, and is validated by comparing numerical results against experimental data.

Integration of brake block thermal equations within a railway vehicle multibody model: a multiphysics approach

ABSTRACT The paper shows the development of a finite-difference (FD) railway brake block thermal model and its integration within the multibody (MB) formalism of the Simpack commercial code. The block nodal temperatures are included among the dynamic states computed by the MB solver, through the definition of a user-defined force element, which determines the braking torque based on the applied brake cylinder pressure. The proposed approach overcomes the main limitations of existing detailed railway vehicle models, which solve the thermal and vehicle dynamics equations in different computational environments. Furthermore, the new strategy can thrust the development of models able to account for the coupling between the wheel and block thermal behaviour and the whole vehicle dynamics. Preliminary simulations of drag and stop braking operations of a reference European freight waggon prove that the proposed model is able to effectively consider the main heat fluxes and nonlinearities involved in tread braking operations.

A hydroelasticity analysis of a damaged ship based on a two-way coupled CFD-DMB method

This study focuses on the numerical investigation of the hull girder loads on a flexible containership S175 with intact and damaged conditions advancing in regular head waves. In this study, a two-way coupled fluid-structure interactions framework is applied, in which the interactions between the flooding water inside the damaged tanks and wave fields are modelled by a Computational Fluid Dynamics toolbox OpenFOAM. The structural deformation is predicted using a multibody solver MBDyn. Hydroelasticity computations are performed for two different damage scenarios. The numerical results obtained show that the damaged ship experiences less vertical motions but greater global wave loads than the intact ship. It is also demonstrated that ship damages greatly influence the hull girder vertical bending moments (VBMs), while still water VBM is sensitive to the added weight from flooding water. In specific ship-damage conditions, local hogging moments at several amidship sections are found to exceed the limits specified by international regulations. Therefore, a new safety factor is recommended to avoid hogging moments of damaged ships remain below the limiting value. The results can also be used to determine whether the damaged ship will experience secondary damage due to hydroelastic response, helping with the design of future conventional ships.

Synthesis and optimization of an eight-bar linkage mechanism for seat suspensions

The work presents the analysis and synthesis of an eight-link mechanism for industrial seat suspension, followed by a numerical optimization of the design under specific technical requirements. Even though the eight-bar linkage mechanism is a well-known architecture, it has few applications in seat suspensions, and it shows interesting features compared with more traditional scissor systems. It is possible to exploit this mechanism, provided that is correctly designed, to achieve a seat suspension system, which grants a large quasi-perfect vertical motion, without the need of prismatic couplers, which are often a weak point in off-highway application due to their maintenance issues and cost. Firstly, the problem was tackled analytically in order to obtain the general set of equations and verified numerically with a multibody solver. Secondly, to choose the best solution for the application, we carried out an optimization of the system, aimed at minimizing the horizontal displacement of the seat along with granting the desired vertical travel needed. The results are both a general design procedure to optimize under specific constraints the eight-bar linkage for seat suspensions problems and a detailed design and possible embodiment of a seat suspension systems with application in the agricultural field.

Performance of implicit A-stable time integration methods for multibody system dynamics

This paper illustrates the performance of several representative implicit A-stable time integration methods with algorithmic dissipation for multibody system dynamics, formulated as a set of mixed implicit first-order differential and algebraic equations. The integrators include the linear multi-step methods with two to four steps, the single-step reformulations of the linear multi-step methods, and explicit first-stage, singly diagonally-implicit Runge–Kutta methods. All methods are implemented in the free, general-purpose multibody solver MBDyn. Their formulations and implementation are presented. According to the comparison from linear analysis and numerical experiments, some general conclusions on the selection of integration schemes and their implementation are obtained. Although all of these methods can predict reasonably accurate solutions, the specific advantages that each of them has in different situations are discussed.

Investigation into the control strategy for a long spine of Edinburgh Duck modules, using an efficient numerical model

An efficient numerical model of a spine of ten Edinburgh duck modules is developed. The spine joints and duck modules are modelled using a linear approach based on the theory of generalized modes, which mitigates the need for a more computationally expensive time- domain solver. This approach also allows for computation of the shear forces acting on the spine joints, and has the added benefit of enabling the use of complex conjugate control. The resulting hydrodynamic model is verified for a three duck spine against an alternative implementation that uses a nonlinear multibody solver to enforce the joint motions. A conservative weighted motion constraint is imposed on the controlled degrees of freedom of the ten duck spine, in order to ensure results stay within the bounds of the linear theory. Pertinent sections of the theory underpinning the constrained complex conjugate control method are elaborated upon for the case in which not all degrees of freedom are controlled. An implementation of this control method for a solo duck is compared against a result from the literature, in order to confirm the suitability of the choice of duck design in this study. The control force coefficients that maximise the absorbed power, subject to the motion constraint, are computed for the ten duck spine over a range of wave periods and wave heading angles. The resulting dynamics of the spine of ducks are explored, with particular emphasis on aspects related to the power extraction and forces acting within the system.

Effect of conventionally neutral boundary layer height on turbine performance and wake mixing in offshore windfarms

In this study, we investigate the effect of conventionally neutral boundary layer height and capping inversion strength on wind farm performance. An aeroelastic multibody solver coupled with a pseudo-spectral large eddy simulation code is used to investigate the structural and aerodynamic output of wind turbines in 4 different inflow types. Farm layouts comprising of turbines in both aligned and staggered arrangements are studied. It is found that the shallower boundary layers with strong capping inversions are characterized by oscillatory structures in turbine wakes, leading to increased structural damage in downstream wind turbines due to fatigue. The power output is also observed to decrease due to poorer wake mixing.

Implementation of the BEM skewed-wake model within the multibody aero-elastic solver Cp-Lambda

To account for the problem of an azimuthally constant induction in the BEM method, which influences on incorrectly predicted aerodynamic loads in the yawed flow, a skewed-wake model implementation to the BEM method has been performed. The numerical aerodynamic loads have been compared with the wind tunnel data of the NREL Phase VI and against another numerical campaign. At first, the model predictions have been validated against experimental data performed with aligned flow conditions, showing a reasonable match. Successively, the model predictions are validated against experimental results obtained with the wind turbine yawed. Results show, a possible better prediction of loads at yawed flow with Skewed-Wake correction, however the method does not overall correlate better, compared to the BEM method with implemented local variability of the induction factor.

A numerical tool for modelling oscillating wave surge converter with nonlinear mechanical constraints

Mechanical constraints have a non-negligible influence in the motion of oscillating wave surge converter (OWSC) devices. The key novelty of this paper is a numerical simulation tool for OWSCs that does not neglect or significantly compromise mechanical constraints such as hydraulic power take-off (PTO) system, revolute joints and frictional contacts among components. The paper is aimed at presenting the key components of the numerical simulation tool and at validating it with laboratory data featuring an OWSC with mechanical constraints under regular and irregular waves. It is based on the implementation of the multibody solver of Project Chrono under the Smoothed Particle Hydrodynamics (SPH) model of DualSPHysics, where the SPH solver resolves the interaction between wave and flap and the multibody solver resolves the interaction between flap and mechanical constraints. Comparison between numerical results and experimental data show that the numerical simulation tool properly predicts the dynamics of the OWSC. Furthermore, in what concerns hydrodynamics of the near-flap flow, the computed and measured free-surface elevations and phase-averaged flow field show reasonable agreement. Once properly validated, the numerical simulation tool is then applied to study the influence of several mechanical constraints, PTO damping characteristics and flap inertia on the hydrodynamic of the OWSC. The viability of OWSC design solutions based on the developed numerical simulation tool is emphasised, in view of its performance in the test cases to which it was subjected.

Transmission Error and strain analysis of lightweight gears by using a hybrid FE-analytical gear contact model

Abstract In this paper the transmission error and the strain field are analysed for two gear pairs, with different lightweight designs, reflecting the common industrial practice. The methodology used for the analysis is based on a hybrid FE-Analytical approach implemented in a multibody solver which allows to achieve a good accuracy with a low computational effort. The specific formulation allows to well describe the deformation field of the gear body from which the strain values can be computed at specific locations in the FE model. The numerical method used in this work is validated both in terms of transmission error and strain field, using the results obtained from an experimental campaign performed on a high-precision gear test rig.

Study of the possible relationships between tramway front-end geometry and pedestrian injury risk

Objectives: The aim of this article is to report on the possible relationships between tramway front-end geometry and pedestrian injury risk over a wide range of possible tramway shapes.Methods: To study the effect of tramway front-end shape on pedestrian injury metrics, accidents were simulated using a custom parameterized model of tramway front-end and pedestrian models available with the MADYMO multibody solver. The approach was automated, allowing the systematic exploration of tramway shapes in conjunction with 4 pedestrian sizes (e.g., 50th percentile male or M50).Results: A total of 8,840 simulations were run, showing that the injury risk is more important for the head than for other body regions (thorax and lower extremities). The head of the M50 impacted the windshield of the tramway in most of the configurations. Two antagonist mechanisms affecting impact velocity of the head and corresponding head injury criterion (HIC) values were observed. The first is a trunk rotation resulting from an engagement of the lower body that can contribute to an increase in head velocity in the direction of the tram. The second is the loading of the shoulder, which can accelerate the upper trunk and head away from the windshield, resulting in lower impact velocities. Groups of design were defined based on 2 main parameters (windshield height and offset), some of which seem more beneficial than others for tramway design. The pedestrian size and tramway velocity (30 vs. 20 km/h) also affected the results.Conclusions: When considering only the front-end shape, the best strategy to limit the risk of head injury due to contact with the stiff windshield seems to be to promote the mechanism involving shoulder loading. Because body regions engaged vary with the pedestrian size, none of the groups of designs performed equally well for all pedestrian sizes. The best compromise is achieved with a combination of a large windscreen offset and a high windscreen. Conversely, particularly unfavorable configurations are observed for low windshield heights, especially with a large offset. Beyond the front-end shape, considering the stiffness of the current windshields and the high injury risks predicted for 30 km/h, the stiffness of the windshield should be considered in the future for further gains in pedestrian safety.

A novel 3D variational aeroelastic framework for flexible multibody dynamics: Application to bat-like flapping dynamics

We present a novel three-dimensional (3D) variational aeroelastic framework for flapping wing with a flexible multibody system subjected to an external incompressible turbulent flow. The proposed aeroelastic framework consists of a three-dimensional fluid solver with a hybrid RANS/LES model based on the delayed detached eddy simulation (DDES) treatment and a nonlinear monolithic elastic structural solver for the flexible multibody system with constraints. Radial basis function (RBF) is applied in this framework to transfer the aerodynamic forces and structural displacements across the discrete non-matching interface meshes while satisfying global energy conservation. For the consistency of the interface data transfer process, the mesh motion of the fluid domain with large elastic deformation due to high-amplitude flapping motion is also performed via the standard radial basis functions. The fluid equations are discretized using a stabilized Petrov–Galerkin method in space and the generalized-α approach is employed to integrate the solution in time. The flexible multibody system is solved by using geometrically exact co-rotational finite element method and an energy decaying scheme is used to achieve numerical stability of the multibody solver with constraints. A nonlinear iterative force correction (NIFC) scheme is applied in a staggered partitioned iterative manner to maintain the numerical stability of aeroelastic coupling with strong added mass effect. An isotropic aluminum wing with flapping motion is simulated via the proposed aeroelastic framework and the accuracy of the coupled solution is validated with the available experimental data. We next study the robustness and reliability of the 3D flexible multibody aeroelastic framework for an anisotropic flapping wing flight involving battens and membranes with composite material and compare against the experimental results. Finally, we demonstrate the aeroelastic framework for a bat-like wing and examine the effects of flexibility on the flapping wing dynamics.

Animation of crack propagation by means of an extended multi-body solver for the material point method

We propose a multi-body solver that extends the Material Point Method (MPM) to simulate cracks in computer animation. We define cracks as the intersection between pieces of bodies created by a pre-fracture process and held together by massless particle constraints (glue particles). These pieces are simulated using a MPM multi-body solver extended by us to efficiently handle N-body collisions. Benefits of the present work include (1) low computational overhead compared to a normal MPM algorithm; (2) good scaling in three dimensions due to our use of sparse grids for background computations; (3) allowing for an easy and controllable setup phase to simulate a desired material failure mode, which is especially useful for computer animation.

ANALYSIS OF CONTROLLED MECHANISM WITH SIGNIFICANT NONLINEARITIES

Solving inverted pendulum by co-simulation between multi-body solver MotionSolve and signal processing control in solidThinking Activate. The simula- tion of inverted pendulum uses an innovative model of friction which is physically and mathematically more accurate than usual CAE friction models. This model of friction adds nonlinearity to the system. Two types of controlling mechanism for active balancing of inverted pendulum are used: PID and ANN controller. A non-traditional false angular deviation approach for returning a cart to its initial position was used.

A formulation of kinematic constraints imposed by kinematic pairs using relative pose in vector form

This paper presents a formulation that expresses kinematic pairs in form of holonomic constraints as functions of a measure of the relative position and orientation of the connected bodies expressed in vector form. While formulating the relative position measure is straightforward, expressing a suitable measure of the relative orientation requires some care. The problem is addressed by computing the Euler vector of the product of the actual and prescribed relative rotation matrices. By arbitrarily combining the error measures in up to six independent equations, a general family of holonomic rheonomic constraints can be formulated. The relative motion between the bodies can be constrained or specified component-wise, respectively, resulting in scleronomic or rheonomic constraints. The proposed formulation is implemented in a free, general-purpose multibody solver; numerical applications to generic mechanical and aerospace problems are presented.

Reduced Order Models Using Generalized Eigenanalysis

This article discusses the use of generalized eigenanalysis to extract reduced order models from the linearization of structural and aeroelastic problems written in differential-algebraic form. These problems may arise from multi-body analysis and in general from mixed approaches, where a high degree of generality and modelling flexibility are sought. A method based on a shift technique is proposed, that allows to exploit the regularity of the matrix pencil resulting from the linearization of differential-algebraic problems. Alternatively, the generalized Schur decomposition, or QZ decomposition, is directly used to select a cluster of eigenvalues related to the dynamic states. The two approaches are used to reduce the model to ordinary differential in state-space form. The two methods are applied to simple numerical problems, highlighting their robustness and versatility compared to other techniques. They are also applied to numerical models of a high-altitude long endurance aircraft obtained using a free general-purpose multi-body solver and a dedicated mixed variational solver.

A computational model for articulated human body dynamics

We developed a novel computational model for articulated human body dynamics, which utilises anatomical geometry of human body for biomechanical simulations. The articulated human body dynamics is computed by an implicit multi-body solver. The exact linearisation of the weak form was carried out to guarantee a quadratic rate of convergence. The developed solver enforces the kinematic constraints well while imposing no limitation on the time step size. The main advantage of the model is the anatomical surface representation of a human body which can accurately account for both the surface loading and the surface interaction. The inertial properties are calculated using a finite element method. To study the articulated human body dynamics under a blast wave loading, we developed an interface to apply the loading resulted from a gas dynamics simulation. The numerical results show that the model is capable of realistically predicting the human body dynamics and can be used to study primary injury mechanism.

Dynamic simulation of virtual prototypes in immersive environment

Virtual reality (VR) became a very common mean during the development of the industrial products. One of the main applications of VR in the industrial field is the validation of virtual prototypes (VP). A virtual prototype should be able to reproduce, as realistically as possible, the behaviour of the product from any point of view. In this paper we propose an unexploited approach to the simulation of a VP in VR. A high level software library for the inter-process communication has been developed to let the multi-body solver communicate with the VR environment. Such approach allows the designer to use different software frameworks for the simulation and the visualisation. The test case provided regards an excavator machine. It is possible to simulate the action of the actuators to move arms and bucket, and also perform visibility analyses discovering the viewing volume of the operator.